Controlling process instability for defect lean metal additive manufacturing

The process instabilities intrinsic to the localized laser-powder bed interaction cause the formation of various defects in laser powder bed fusion (LPBF) additive manufacturing process. Particularly, the stochastic formation of large spatters leads to unpredictable defects in the as-printed parts. Here we report the elimination of large spatters through controlling laser-powder bed interaction instabilities by using nanoparticles. The elimination of large spatters results in 3D printing of defect lean sample with good consistency and enhanced properties. We reveal that two mechanisms work synergistically to eliminate all types of large spatters: (1) nanoparticle-enabled control of molten pool fluctuation eliminates the liquid breakup induced large spatters; (2) nanoparticle-enabled control of the liquid droplet coalescence eliminates liquid droplet colliding induced large spatters. The nanoparticle-enabled simultaneous stabilization of molten pool fluctuation and prevention of liquid droplet coalescence discovered here provide a potential way to achieve defect lean metal additive manufacturing.

Supplementary Figure 10. The packing requirement of nanoparticles on spatter surface for controlling spatter coalescence. a, Schematic showing that close packing of nanoparticles on spatter surface prevents coalescence. b, Schematic showing that the colliding between two exposed surfaces of liquid spatters induces coalescence. c, Schematic showing the colliding between exposed spatter surface and coated spatter surface. d, The effect of interparticle spacing on capillary pressure barrier. The nanoparticle distance in d is defined as the center-to-center distance of two nearest nanoparticles on the spatter surface. e, The effect of number of nanoparticle layers between two spatters on capillary pressure barrier.

Supplementary
Viscosity (mPa s) and bare substrate (for x-ray imaging experiment without powder layer) were cut from the as- × 1 mm (thickness) developed for additively manufactured metal (MT2) in reference 2 was used in the tensile test. Smaller samples (than ASTM E8 standard) were used because (1) smaller sample enables us to study the effect of printing position on property variation within one build; (2) the printed area is relatively small (25 mm × 25 mm) for our self-designed LPBF system. To make the tensile test results comparable, we also used the same sample size for tensile testing of the commercial Al6061.

Supplementary Note 2: Estimation of the volume fraction of TiC
Since TiC is relatively stable in the Al6061 melt with negligible reaction 3,4 (which is confirmed by XRD results in the Supplementary Fig. 2) and the Ti content in Al6061 powder is negligible, the volume fraction of TiC nanoparticles (VTiC) was estimated based on the weight fraction of Ti in the as-printed sample by the following equation: where WTiC is the weight fraction of TiC in the as-printed Al6061+TiC sample. WTi is the weight fraction of Ti (6.3%), which was determined by ICP test (the whole sample, including TiC nanoparticles, is fully dissolved during ICP test). ρ TiC is the density of TiC (4930 kg m -3 ). ρ nc is the density of the Al6061+TiC, which was calculated by the following equation: where ρAl is the density of Al6061 (2705 kg m -3 ). Since the density of Al6061+TiC is related to the volume fraction of TiC, Equation (1) and (2) were solved iteratively until the volume fraction value stabilizes. The calculated volume fraction of TiC is 4.4%.

Supplementary Note 3: Effects of powder morphology on laser-powder interaction
Since

Supplementary Note 4: Effects of surface tension and viscosity on vapor depression stability
To understand the underlying mechanism of nanoparticle-enabled stabilization of vapor depression, we measured the surface tension and viscosity of Al6061 and Al6061+4.4vol.%TiC and performed laser melting simulation (see Supplementary Note 5) with measured surface tension and viscosity value as input to study their effects on vapor depression dynamics.
The surface tension and viscosity were measured based on the oscillating droplet method 8 , as schematically shown in Supplementary Fig. 7a. During the test, the sample (cut from commercial Al6061 plate or as-printed Al6061+TiC sample) was placed on top of an inert ring (which holds the droplet) with an inner diameter of 2 mm and thickness of 0.5 mm. A continuous-wave ytterbium fiber laser (IPG YLR-500-AC, IPG Photonics, USA) was used to melt the sample with a weight of 1.3 × 10 -2 g corresponding to a sphere with a diameter of 2.2 mm using a laser power of 150 W, laser beam size (D4σ) of 250 µm, and heating time of 2 s. After melting, the linear solenoid was immediately triggered to accelerate the ring, which forces the liquid droplet to flow through the ring and introduces the initial deformation. The oscillation of the droplet after leaving the ring was captured by a high-speed visible light camera (FASTCAM Nova S12) at a frame rate of 10 kHz. The oscillation frequency is used to calculate the surface tension: where σ is the surface tension, m is the mass of the droplet, f is the oscillation frequency. The damping speed of the amplitude during oscillation is used to calculate the viscosity: where μ is the viscosity, d 0 is the equilibrium diameter of the droplet, t is the oscillation time, ζ 0 is the initial amplitude, ζ is the amplitude at oscillation time t. The amplitude is determined from the vertical diameter of the droplet versus time curve in the Supplementary Fig. 7b. Based on the amplitude and frequency of the droplet oscillation, the calculated viscosity of the Al6061+4.4vol.%TiC (79.4 mPa·s) is 15 times higher than that of the Al6061 (4.9 mPa·s). The calculated surface tension of the Al6061+4.4vol.%TiC (0.81 N·m -1 ) is 19% higher than that of the Al6061 (0.68 N·m -1 ).
The measured values were then imported into simulation to study the effect of surface tension and viscosity on the vapor depression dynamics (Supplementary Fig. 8). Four simulations with different surface tension and viscosity combinations were performed (Supplementary Table 3 (Fig. 3k). The viscous stress is proportional to the viscosity and velocity gradient, as depicted in the following equation: where τ is the viscous shear stress; µ is the viscosity; v is the moving velocity of vapor depression front wall induced by depression fluctuation, x is the distance along the vapor depression front wall, v c is the front wall moving velocity at the center of the fluctuation, h is the distance from center to the edge of the fluctuation (Fig. 3k, l). Due to the increased viscosity (μ) by nanoparticles, smaller front wall moving velocity (v c ) is needed for generating the same viscous stress to resist recoil pressure (Pr). Therefore, the depth of the fluctuation (d = v c ∆t, where ∆t is the time period and is considered constant to study the deformation within a same time period) decreased, resulting in the stabilization of vapor depression.

Supplementary Note 5: Computational thermo-fluid dynamics simulation
The vapor depression dynamics during laser melting process was simulated by FLOW-3D (FLOW-3D 12.0, Flow Sciences, USA). Throughout the simulation, the flow is assumed to be laminar and Newtonian. Governing equations include the continuity equation, momentum conservation equation and energy conservation equation: where ρ is the density, v (⃗ is the velocity vector, μ is the viscosity, t is the time, p is the pressure, g (⃗ is the gravitational acceleration vector, q is the heat source, k is the thermal conductivity, h is enthalpy, which is calculated as: where ρ s is the density at solid state, C s is the specific heat at solid state, T is the temperature, h sl is the latent heat of melting, T s is the solidus temperature, T l is the liquidus temperature, ρ l is the density at liquid state, C l is the specific heat at liquid state. The free surface is tracked by the Volume of Fluid (VOF) method, as denoted by the following equation: where F is the phase fraction. Thus, fluid exists within regions of 'F = 1', whilst 'F = 0' corresponds to regions considered as voids with uniform pressure. The interface reconstruction is carried out using the split Lagrangian scheme.
The multiple reflection model based on ray-tracing technique is implemented in the simulation.
For each incidence, and absorption is calculated by the Fresnel equation: where θ is the incident angle; ε is a constant related to the material and laser properties, which was calibrated by experimental data captured by x-ray imaging (length and depth of melt pool, depth of vapor depression).
To study the vapor depression dynamics, the recoil pressure, which is the major driving force for vapor depression formation, is considered based on the following equation: where P 0 is the ambient pressure, λ is the latent heat of vaporization, K B is the Boltzmann constant, T is the surface temperature, T b is the boiling temperature. Other driving forces including thermocapillary force, gravity force and buoyancy force are also considered in the model. The properties of Al6061 used in simulation are presented in Supplementary Table 4. The dimension of the Al6061 plate in simulation is 3 mm (length) × 0.7 mm (width) × 0.5 mm (depth) with an initial temperature of 298 K. The mesh size is 4 µm.

Supplementary Note 6: Guideline for estimating nanoparticle volume fraction needed for controlling spatter coalescence
To control spatter coalescence and eliminate large spatters, we proposed that nanoparticles should form a close packing on metal powder/spatter surface. If nanoparticles are not closely packed, it is likely to generate an exposed surface area without nanoparticles (Supplementary Fig.   10b). If two exposed surfaces come into contact during spatter colliding, the spatters can easily coalesce. This is also confirmed by the capillary pressure model, based on which the effects of interparticle spacing on the capillary pressure were calculated (assuming contact angle of 52°).
The results ( Supplementary Fig. 10d) show that there is a sudden drop of capillary pressure barrier when the interparticle distance starts to increase (capillary pressure decreases by 51% when the ratio of interparticle distance to nanoparticle diameter increases from 1.05 to 3). This will increase the possibility of spatter coalescence.
If only one spatter has closely packed nanoparticles, while another one has exposed surface area ( Supplementary Fig. 10c), there will be only one-layer nanoparticle between two liquid spatters.
The capillary pressure barrier generated by one-layer nanoparticle (based on capillary pressure model) is significantly weaker than that generated by two layers (Supplementary Fig. 10e). For example, the highest temperature at which the capillary pressure overcomes the initial pressure decreases from 1420 K for two-layer nanoparticle to 1159 K for one-layer nanoparticle. Therefore, for all spatters, the one-layer close packing of nanoparticles on the surface is required.
To guide the material design, we developed an equation to calculate the volume fraction of nanoparticles needed for close packing based on the relationship between nanoparticle crosssection area and metal powder surface area: where f is the nanoparticle surface converging fraction (the projection areas of the nanoparticles to the surface area of the spatter) for close packing (here assumed f = 0.907 for hexagonal close packing). N m is the number of metal powders, A m is the surface area of metal powder, N n is the number of nanoparticles, A n is the cross-section area of nanoparticle. The number of metal powder/ceramic particle (N m , N n ) in Equation (13) can be calculated by dividing the total volume by the volume of single metal powder/ceramic particle. Therefore, Equation (13) can be written as: V is the volume fraction of nanoparticles. r m is the radius of metal powder; r n is the radius of nanoparticle. Assuming metal powder size is much larger than nanoparticle size, based on equation (14), the volume fraction of nanoparticles can be expressed as: It should be noted that given the nanoparticles may be not uniformly dispersed on the metal powder surface, the calculated volume fraction of nanoparticles is a minimum number.